Finding a point part way between two points | Analytic geometry | Geometry | Khan Academy | Summary and Q&A

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December 11, 2013
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Finding a point part way between two points | Analytic geometry | Geometry | Khan Academy

TL;DR

Find point B on segment AC such that the ratio of AB to BC is 3:1.

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Questions & Answers

Q: How can the problem of finding point B be approached?

The problem can be approached by breaking it down into horizontal and vertical changes between points A and C. We can calculate the horizontal and vertical distances separately to find B.

Q: What are the horizontal and vertical distances between points A and C?

The horizontal distance between A and C is 16 units, while the vertical distance is 4 units.

Q: How can we determine the coordinates of point B?

To find the coordinates of point B, we need to move 1/4 of the way from C to A both vertically and horizontally. This will result in the coordinates (-3, 2) for point B.

Q: How can we visually determine the position of point B on the line segment?

We can visually determine the position of point B by marking the 1/4 distance on either the horizontal or vertical axis and finding the intersection point on the line segment.

Summary & Key Takeaways

  • The task is to find point B on segment AC, with a specific ratio of AB to BC.

  • The distance between B and A is 3 times the distance between B and C.

  • The problem can be solved by breaking it down into vertical and horizontal changes between point A and point C.

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